Each of the documents listed below is referred to herein by the corresponding number enclosed in square brackets to the left of the document. Each of these documents is also incorporated herein by reference.
[1] E. Biglieri, D. Divsalar, P. J. McLane, and M. K. Simon, Introduction to Trellis Coded Modulation with Applications. MacMillan, 1991.
[2] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding: Turbo codes,” Proc. 1993 IEEE International Conference on Communications ICC, pp. 1064–1070, 1993.
[3] S. L. Goff, A. Glavieux, and C. Berrou, “Turbo-codes and high spectral efficiency modulation,” Proc. 1994 IEEE International Conference on Communications ICC, pp. 645–649, 1993.
[4] A. J. Viterbi, E. Zehavi, R. Padovani, and J. K. Wolf, “A pragmatic approach to trellis-coded modulation,” IEEE Commun. Mag., pp. 11–19, July 1989.
[5] P. Robertson and T. Worz, “A novel bandwidth efficient coding scheme employing turbo codes,” Proc. 1996 IEEE International Conference on Communications ICC, pp. 962–967, 1996.
[6] P. Robertson and T. Worz, “Bandwidth-efficient turbo trellis-coded modulation using punctured component codes,” IEEE JSAC, pp. 206–218, February 1998.
[7] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “Parallel concatenated trellis coded modulation,” Proc. 1996 IEEE International Conference on Communications ICC, pp. 974–978, 1996.
[8] S. Benedetto and G. Montorsi, “Design of parallel concatenated convolutional codes,” IEEE Trans. Commun., pp. 591–600, May 1996.
[9] O. Y. Takeshita, O. M. Collins, P. C. Massey, and D. J. Costello, “On the frame error rate of turbo-codes,” Proceedings of ITW 1998, pp. 118–119, June 1998.
[10] O. Y. Takeshita, O. M. Collins, P. C. Massey, and D. J. Costello, “A note on asymmetric turbo-codes,” IEEE Communications Letters, vol. 3, pp. 69–71, March 1999.
[11] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “A soft-input soft-output APP module for interative decoding of concatenated codes,” IEEE Commun. Lett., pp. 22–24, January 1997.
Trellis-Coded Modulation (TCM) has been demonstrated in [1] to offer a substantial coding gain without requiring bandwidth expansion. This is achieved by appropriate joint design of coding and modulation. Turbo codes, also known as parallel concatenated convolutional codes (PCCC), were initially proposed in [2], and have been known to attain very low error rates within the signal-to-noise ratio (SNR) range close to the Shannon limit. Attempts have therefore been made to combine TCM and turbo codes to obtain a class of powerful bandwidth-efficient coded modulation schemes. One such attempt was reported in [3]. The arrangement described in [3] uses the structure of the pragmatic TCM proposed in [4]. Schemes with improved performance were later proposed in [5], [6] and [7].
The original turbo code proposed in [2] utilizes two identical recursive systematic component codes (RSCCs) in parallel concatenation with an interleaver. This turbo code attains excellent bit-error rate (BER) for low SNR values. As the SNR increases, the BER drops very quickly. However, after a certain SNR value, there is a sudden reduction in the rate at which the BER drops. This phenomenon, referred to in [8], [9] and [10] is known as the “error floor”.
It is demonstrated in [9] and [10] that the error floor for the original turbo code of [2] occurs at 10−5 for a length-16384 interleaver. Such an error floor is not desirable for high quality data communication applications such as, for example video communications for a wireless personal area network (WPAN). Such applications can require a BER of, for example, 10−8. Although the error floor for the original turbo code can be lowered, for example, by choosing a larger interleaver size, such an adjustment disadvantageously increases system complexity and latency.
Several attempts have been made to lower the error floor without increasing the interleaver size. For example, it is shown in [8] that the error floor can be lowered by choosing the feedback polynomial of the component codes to be primitive. This essentially increases the effective Hamming distance of the turbo code (which is known from [8] to be a good measure of code performance). However, as the error floor goes down, the BER in the low SNR region (referred to herein as the waterfall region) increases (see [9] and [10]).
The authors of [9] and [10] attempted to provide for a trade-off between a low error floor and good performance in the waterfall region. In this regard, they suggested an asymmetric turbo coding structure wherein one component code has a non-primitive feedback polynomial (as in the original turbo code of [2]), and the other component code has a primitive feedback polynomial. An example of this coding structure, referred to in [9] and [10] as an asymmetric PCCC, is illustrated in FIG. 1. In the example of FIG. 1, the upper component code (RSCC 1) is a rate ½ RSCC with a primitive feedback polynomial, and the lower component code (RSCC 2) is a rate ½ RSCC with a non-primitive feedback polynomial. The systematic of the lower code is punctured, so the asymmetric PCCC produces coded bit outputs C1 and C2 from the upper branch and C3 from the lower branch.
FIG. 2 illustrates a conventional example of a parallel concatenated trellis-coded modulation (PCTCM) structure. In the example of FIG. 2, the RSCC 25 and mapping 26 for the upper and lower branches are identical. This type of structure is referred to herein as symmetric mapping PCTCM. In conventional structures such as shown in FIG. 2, the PCTCM is typically designed using the conventional approach of searching for a component code that has good properties for a given mapping (see [6] and [7]). Typical examples of conventional mappings that are used in arrangements like FIG. 2 include natural (set partitioning) mapping and Gray mapping. The coded bits from each component RSCC are mapped into signals S1 and S2 that take values within a constellation. For PCTCM, the search criterion is to maximize the effective Euclidean distance of the trellis code (see [7]). Like PCCC, PCTCM does not always provide a low enough error floor for some applications (such as the aforementioned video communication applications for WPAN). This can occur in PCTCM even when a component code that results in maximum effective Euclidean distance of the trellis code has been identified for a given mapping. This is especially true when an interleaver of moderate size is utilized.
FIG. 3 illustrates a specific example of the PCTCM structure shown in FIG. 2. The example of FIG. 3 is a 2 bps/Hz PCTCM system for 16-QAM. U1 and U2 represent uncoded bits from a communication application. The upper (X2 and X1) and lower (Y2 and Y1) coded bits are mapped onto a 4-PAM constellation to form in-phase (I) and quadrature (Q) components, which are combined (e.g. summed) at 31 to produce the 16-QAM signal. Two different length K-bit interleavers π1 (for LSB U1) and π2 (for LSB U2) are used in FIG. 3 to implement the interleaver section 27 of FIG. 2. As an example, K=4096. The rate-1 RSCC G(D) with maximum effective Euclidean distance for Gray mapping (see FIG. 5) is used. FIG. 4 illustrates an example of the G(D) of FIG. 3. In particular, the G(D) shown in FIG. 4 is the “best” 8 state RSCC G(D) for Gray mapping, and is disclosed in [7]. (The FIG. 4 G(D) was used for both transmitter branches in all simulations described herein.)
Another possibility for the mapping in FIG. 3 is conventional 0231 mapping, as illustrated in FIG. 6. Again, a search could be conducted for a RSCC G(D) with good properties for the 0231 mapping.
FIG. 3A illustrates another example of the structure of FIG. 2. FIG. 3A uses identical QPSK (or 8PSK) mappings at 26, and the results of the mappings are applied to a parallel-to-serial converter before transmission.
In each of the examples of FIGS. 3 and 3A, the G(D) for one branch can differ from the G(D) for the other branch.
With respect to the example of FIG. 3, FIGS. 7 and 8 illustrate exemplary simulation results using Gray mapping and 0231 mapping, respectively, for h0=13, h1=17, h2=15 and K=4096, and assuming an additive white Gaussian noise (AWGN) channel with a power spectral density of N0. The simulations of FIGS. 7 and 8 plot the BER as a function of the uncoded SNR per bit, or Eb/N0. The simulations of FIGS. 7 and 8 use the iterative MAP decoding algorithm for PCTCM found in [11], and results for 2, 4, 6 and 8 iterations are shown. In FIG. 7 (Gray mapping), the error floor occurs at around BER=10−7. Thus, and although the Gray mapping system provides excellent performance in the waterfall region, nevertheless it does not meet the aforementioned requirement of BER=10−8. In FIG. 8 (0231 mapping), the error floor is greatly reduced and is clearly below the aforementioned target of BER=10−8. However, the BER in the waterfall region is significantly higher than in FIG. 7.
It is desirable in view of the foregoing to provide for a PCTCM system that can achieve acceptable performance in the waterfall region while also achieving an error floor that is acceptable for high quality data communication applications.
According to the invention, an error floor suitable for high quality data applications can be advantageously achieved in combination with acceptable performance in the waterfall region by providing an asymmetric PCTCM system including two component trellis code branches which utilize different coded bits-to-signal mappings.